S U P E R C O N D U C T O R S 2015 © The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. Distributed under a Creative Commons Attribution License 4.0 (CC BY). 10.1126/sciadv.1500568
Unified understanding of superconductivity and
Mott transition in alkali-doped fullerides from
first principles
Yusuke Nomura,1* Shiro Sakai,2Massimo Capone,3Ryotaro Arita2,4
Alkali-doped fulleridesA3C60(A = K, Rb, Cs) are surprising materials where conventional phonon-mediated
super-conductivity and unconventional Mott physics meet, leading to a remarkable phase diagram as a function of volume per C60molecule. We address these materials with a state-of-the-art calculation, where we construct a
realistic low-energy model from first principles without using a priori information other than the crystal structure and solve it with an accurate many-body theory. Remarkably, our scheme comprehensively reproduces the ex-perimental phase diagram including the low-spin Mott-insulating phase next to the superconducting phase. More remarkably, the critical temperaturesTc’s calculated from first principles quantitatively reproduce the
experimen-tal values. The driving force behind the surprising phase diagram ofA3C60is a subtle competition between
Hund’s coupling and Jahn-Teller phonons, which leads to an effectively inverted Hund’s coupling. Our results establish that the fullerides are the first members of a novel class of molecular superconductors in which the multiorbital electronic correlations and phonons cooperate to reach highTcs-wave superconductivity.
INTRODUCTION
Alkali-doped fullerides are unique exotics-wave superconductors
with maximum critical temperatureTc~ 40 K, which is extremely
high for the modest width of about 0.5 eV of the bands relevant to
superconductivity (1–9). Although the evidence for a phononic pairing
mechanism is robust and may suggest a conventional explanation for
the superconductivity in these materials (2), the experimental
obser-vation of a Mott-insulating phase next to the superconducting phase in
Cs3C60changes the perspective because the same strong correlations
responsible for the Mott state are also likely to influence the
supercon-ducting state (3–9). This raises the fundamental question of why s-wave
superconductivity, which is induced by some attractive interaction, is so
resilient to (or even enhanced by) the strong repulsive interactions (2).
The fingerprints of phonons observed in the Mott-insulating phase,
such as the low-spin state (4–9) and the dynamical Jahn-Teller effect
(10), confirm a nontrivial cooperation between the electron
correla-tions and the electron-phonon interaccorrela-tions.
A variety of scenarios have been proposed to explain the
super-conductivity (2, 11–21). However, even the most successful theories
include some adjustable parameter and/or neglect, for example, the realistic band structure, the intermolecular Coulomb interactions, and
Hund’s coupling. These assumptions have prevented these theories
from being conclusive on the superconducting mechanism, which arises from a subtle energy balance between the Coulomb and the electron-phonon interactions in a multiorbital system. Therefore, to pin down the pairing mechanism, a nonempirical analysis is indispensable: If fully ab initio calculations quantitatively reproduced the phase
dia-gram andTc, they would provide precious microscopic information
to identify unambiguously the superconducting mechanism, opening the path toward a predictive theory of superconductivity in correlated molecular materials.
Here, we carry out such nonempirical analysis using a combination of density functional theory (DFT) and dynamical mean-field theory (DMFT), an approach that accurately describes the properties of many
correlated materials (22). DMFT is particularly accurate for compounds
with short-range interactions and a large coordination numberz, such
asA3C60, a highly symmetric three-dimensional system withz = 12.
RESULTS
Theoretical phase diagram and comparison with experiments In Fig. 1, we show the band structure obtained within DFT for
face-centered cubic (fcc) Cs3C60. Because thet1ubands crossing the Fermi
level are well isolated from the other bands, we construct a lattice
Hamiltonian consisting of thet1uelectron and phonon degrees of
free-dom. The Hamiltonian is defined in the most general form: ℋ ¼
∑
ijksℋ ð0Þ ij ðkÞcs†ikcsjkþqkk′∑
iji∑
′j′∑
ss′Uij;i′j′ðqÞ c s† ikþqcsj′k′′†cs ′ i′k′þqcsjkþ∑
ijks∑
qng n ijðk;qÞcs† ikþqcsjkðbqnþ b†−qnÞ þ∑
qnwqnb†qnbqn; ð1Þon the fcc lattice, where each site represents a C60molecule.ℋð0Þ; U; g,
andw are the electron one-body Hamiltonian, Coulomb interaction,
electron-phonon coupling, and phonon frequency, respectively. They
all have indices of the Wannier orbitalsi, j, i′, j′, spin s, s′, momentum
k,q, and the phonons also have a branch index n. We construct
max-imally localized Wannier orbitals (23) as the basis for making the
hopping and interaction parameters as short-ranged as possible. We determine all of the above parameters by state-of-the-art ab initio tech-niques (Materials and Methods). In particular, the recently developed
constrained density-functional perturbation theory (cDFPT) (24) has
1
Department of Applied Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.2Center for Emergent Matter Science (CEMS), RIKEN, 2-1, Hirosawa, Wako, Saitama
351-0198, Japan.3International School for Advanced Studies (SISSA) and Consiglio
Nazionale delle Ricerche–Istituto Officina dei Materiali (CNR-IOM) Democritos National Simulation Center, Via Bonomea 265, I-34136 Trieste, Italy.4Japan Science and Technology Agency (JST) ERATO Isobe Degenerate -Integration Project, Advanced Institute for Materials Research (AIMR), Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan.
*Corresponding author. E-mail: yusuke.nomura@riken.jp
on May 24, 2017
http://advances.sciencemag.org/
enabled calculations of the phonon-related terms (gijnandwqn), where the effects of the high-energy bands are incorporated into the parameter values. To solve the ab initio model, we used the extended DMFT
(E-DMFT) (22), which combines the ability of DMFT to treat local
interac-tions with the inclusion of nonlocal terms. To study the superconductivity,
we introduced the anomalous Green’s function, whose integral over
frequen-cy gives superconducting order parameter, into the E-DMFT equations. Figure 2A shows the theoretical phase diagram as a function of
temperatureT and volume per C603−anion (VC3
60). As a function of
T and VC3
60, we find a paramagnetic metal, a paramagnetic Mott
in-sulator, and thes-wave superconducting phase where two electrons in
the same orbital form the Cooper pairs. The three phases are charac-terized by a finite spectral weight at the Fermi level, a Mott gap, and
nonzero anomalous Green’s function and order parameter,
respective-ly. The metal-insulator transition is of the first order below 80 K, and a direct first-order superconductor-insulator transition takes place
around VC3
60 ¼ 780 Å
3at low temperature. Between the blue solid line
Vc2(T) and the black dotted line Vc1(T), we find both a metallic and an
insulating solution. The first-order transition lineVc(T), where the free
energies of the two solutions cross, is expected to be close toVc2(T) at
low temperature as in the pure multiorbital Hubbard model (25).
In Fig. 2B, we reproduce the experimental phase diagram (9) for
fccA3C60systems to highlight the impressive agreement with our
cal-culations. In particular, the maximumTcof ~28 K in theory is
com-parable to that of the experiment ~35 K (5, 9). The critical volumes
and the slope of the metal-insulator transition line are also consistent with the experiment. It is remarkable that our fully ab initio calcula-tion, without any empirical parameters, reproduces quantitatively the experimental phase diagram including the unconventional super-conductivity and the Mott insulator.
Unusual intramolecular interactions as a key for unconventional physics
The success of our theory in reproducing the experimental phase di-agram demonstrates the reliability of the whole scheme including the estimates of the interaction parameters. We are therefore in a position to disentangle the crucial ingredients leading to the proximity of the s-wave superconductivity and a Mott insulator in the same diagram. The key quantities are the effective intramolecular interactions
(in-traorbital and interorbital density-density interactionsUeff=U + UV+
UphandU′eff=U′ + U′V+U′ph, and exchange termJeff=J + Jph)
be-tween thet1uelectrons, which are used as input interaction parameters
for the E-DMFT calculation. Here,U, U′, and J are the intramolecular
Fig. 1. Band structure of fcc Cs3C60withVC60
3−= 762 Å3. The blue dotted curves represent the Wannier-interpolated band dispersion calculated from ℋij(0)in Eq. 1.
Fig. 2. Theoretical and experimental phase diagrams. (A) Phase diagram as a function of volume per C60molecule and temperature, obtained with the DFT +
E-DMFT. PM, PI, and SC denote the paramagnetic metal, the paramagnetic insulator, and the superconducting phase, respectively. Metallic and insulating E-DMFT solutions coexist between the blue solid line Vc2(T) and the black dotted line Vc1(T). The error bars for Tcoriginate from the statistical errors in the superconducting order parameters calculated with the quantum Monte Carlo method (see Section E in the Supplementary Materials for details). The error bars for Vc1(T) and Vc2(T)
are half the interval of the volume grid in the calculation. (B) For comparison, the experimental phase diagram [adapted by Y. Kasahara from Figure 6 in Zadik et al. (9)] is shown, where the region depicted in (A) corresponds to the area surrounded by the green dotted lines. AFI denotes the antiferromagnetic insulator.
on May 24, 2017
http://advances.sciencemag.org/
Coulomb interactions screened by the high-energy electrons, whereas
UV=U′VandJV= 0 (Uph,U′ph, andJph) represent dynamical screening
contributions from the intermolecular Coulomb (electron-phonon) in-teractions. These dynamical screening effects make the effective
inter-actions dependent on electron’s frequency w.
The solid curves in Fig. 3 showUeff(w) and U′eff(w), where we find
U′eff(w) > Ueff(w) up to w ~0.2 eV except a narrow region around w =
0.1 eV. This remarkable inversion of the low-energy interactions is
associated with the negative value ofJeff(0) discussed below because
the relationU′eff(w) ~ Ueff(w) − 2Jeff(w) holds. As is apparent from
U > U′ and U + UV>U′ + U′V(plotted by dotted and dashed curves
in Fig. 3), it is the phonon contribution (Uph,U′ph, andJph) that causes
the inversion. In fact,Uph(w) and U′ph(w) have strongly w-dependent
structures forw ≲ 0.2 eV because of the intramolecular Jahn-Teller
phonons with the frequencies up to ~0.2 eV (2), which are comparable
to thet1ubandwidth ~0.5 eV.
Table 1 shows the static (w = 0) values of the phonon-mediated
interactions for variousA3C60compounds. For all the interactions,
the phonon contribution has an opposite sign with respect toU, U′,
andJ. Whereas |Uph(0)| and |U′ph(0)| are much smaller thanU and U′
~1 eV, |Jph(0)| ~51 meV is remarkably larger than that of the positive
Hund’s coupling J ~34 meV (26). As a result, an effectively negative
exchange interactionJeff(0) =J + Jph(0) ~–17 meV is realized. The
unusual sign inversion of the exchange interaction (17, 18, 27, 28)
results from the molecular nature of the localized orbitals, which yields
a smallJ, combined with a strong coupling between the Jahn-Teller
phonons andt1uelectrons (2), which enhances |Jph(0)|.
Microscopic mechanism of superconductivity
We find, through a detailed analysis (Section F in the Supplementary Materials), that the unusual multiorbital interactions indeed drives the
exotics-wave superconductivity: (i) U′eff>UeffandJeff< 0 aroundw = 0
generate a singlet pair of electrons (leading to a Cooper pair) (19),
which sit on the same orbital rather than on different orbitals as shown
by 〈ni↑ni↓〉 > 〈ni↑nj↓〉 in Fig. 4A. (ii) Jefffurther enhances the pairing
through a coherent tunneling of pairs between orbitals [the Suhl-Kondo
mechanism (29, 30)].
As we have discussed above, these unusual multiorbital interactions are caused by phonons. In this sense, phonons are necessary to explain the superconductivity. However, strong electronic correlations also play a crucial role, marking a substantial difference from conventional
phonon-driven superconductivity (17–19): The strong correlations
heavily renormalize the electronic kinetic energy (from a bare value of ~0.5 eV) so that even the small difference (~33 to 37 meV) between
U′effandUeffis sufficient to bind the electrons into intraorbital pairs
(19) [that is, it helps the mechanism (i)]. As a result, Tcincreases with
the correlation strength (seeTcversus VC3
60 in Fig. 2A). This analysis
clearly demonstrates that the superconductivity in alkali-doped fullerides is the result of a synergy between electron-phonon interactions and
electronic correlations (17, 18).
A peculiar low-spin Mott insulator
Also, the normal state displays remarkable consequences of the coop-erative effect of the various interactions. Figure 4A shows the volume
dependence of the intraorbital double occupancyD and the size S of
the spin per molecule atT = 40 K. Here, we follow the metallic
solu-tion, expected to be stable in almost the entire coexistence region (25).
In the Mott-insulating region with the Mott gap in the spectral
function (Fig. 4B),S approaches 1/2 (Fig. 4A), which is of the low-spin
state, in agreement with the experimental observation (4–9). Another
feature characteristic to the present Mott transition is the increase ofD
with the increase of the correlation strength, in sharp contrast with
standard Mott transitions, in whichD is drastically reduced.
This phenomenology also descends fromUeff<U′effandJeff< 0,
which prefer onsite low-spin configurations with two electrons on one orbital (Fig. 4D). In the metallic phase, the electron hopping tends instead to make all the different local configurations equally likely
(Fig. 4C) (19). As the correlation increases, the electrons gradually lose their
kinetic energy, and hence, the six low-spin configurations ({n1,n2,n3} =
{2,1,0}, {0,2,1}, {1,0,2}, {2,0,1}, {1,2,0}, {0,1,2}) become the majority
(Fig. 4C), which leads to the decrease (increase) ofS (D). Eventually, in
the Mott-insulating phase, these configurations become predominant.
Fig. 3. Frequency dependence of effective onsite interactions. The ef-fective intra- and interorbital interactions (Ueff= U + UV+ Uphand U′eff= U′ +
U′V+ U′ph, respectively) consist of the constrained random-phase
approxima-tion (cRPA) onsite Coulomb repulsion (U, U′), the dynamical screening from the off-site interactions (UV= U′V), and the phonon-mediated interactions
(Uph, U′ph). The data are calculated for Cs3C60with VC
60
3−= 762 Å3at 40 K. We
assume the cRPA Coulomb interactions to be static, whose validity is sub-stantiated in Section B in the Supplementary Materials. Inset: Frequency dependence of Ueffand U′effalong the Matsubara frequency axis.
Table 1. Material dependence of the static part of the phonon-mediated interactions. Uph(0), U′ph(0), and Jph(0) are the phonon-mediated onsite
in-traorbital, interorbital, and exchange interaction strengths between the t1uelectrons atw = 0 calculated with the cDFPT. The energy unit is eV.
The numbers just after the material names denote the volume occupied per C603−anion in Å3. Uph(0) U′ph(0) Jph(0) K3C60(722) −0.15 −0.053 −0.050 Rb3C60(750) −0.14 −0.042 −0.051 Cs3C60(762) −0.11 −0.013 −0.051 Cs3C60(784) −0.12 −0.022 −0.051 Cs3C60(804) −0.13 −0.031 −0.052 on May 24, 2017 http://advances.sciencemag.org/ Downloaded from
Remarkably, the six (210) configurations, in each of which the orbital degeneracy is lifted (Fig. 4D), remain degenerate and no orbital ordering occurs. This unusual orbitally degenerate Mott state is consistent with the
experimental observation of a dynamical Jahn-Teller effect (10).
DISCUSSION
We have carried out a fully ab initio study of the phase diagram of alkali-doped fullerides, in which all the interactions of a multiorbital Hubbard model coupled with phonons are computed from first princi-ples with only the information on the atomic positions. The model is then
solved by means of E-DMFT. We identify that a negative Hund’s
cou-pling arising from the electron-phonon interaction and the related
con-ditionUeff<U′effthat favors intraorbital pairs (17, 18, 27, 28) underlie the
existence of the superconducting state, its competition with the low-spin Mott state, and the whole phase diagram, which in turn remarkably re-produces the experimental observations.
This identifies a general condition under which a material can show a high-temperature electron-phonon superconducting phase that
ben-efits from strong correlations (17), and suggests that a wider family of
molecular conductors can exhibit a similar physics as long as an
in-verted Hund’s exchange is stabilized by electron-phonon coupling. In
view of the accuracy demonstrated forA3C60, we can apply the
meth-odology of this article to design other similar materials, possibly tailor-ing their properties to maximize the transition temperature.
MATERIALS AND METHODS
We apply the DFT + DMFT method (22) to fcc A3C60. We start from
the global band structure (Fig. 1) obtained by the DFT (see Section A in the Supplementary Materials for the calculation conditions).
Con-sidering that the low-energy properties are governed by the isolatedt1u
bands, we derive from first principles the lattice Hamiltonian (Eq.1)
for thet1uelectrons and the phonons.
As the basis for the lattice Hamiltonian, we construct the
maximal-ly localized Wannier orbitals (23) {ϕiR} from thet1ubands. We
calcu-late the transfer integrals by tijðRÞ ¼ 〈ϕiRjℋKSjϕj0〉 with the Kohn-Sham
HamiltonianℋKS.ℋð0Þij ðkÞ in Eq. 1 is the Fourier transform of tij(R),
which reproduces the original DFT band dispersion well (Fig. 1). The Coulomb interaction in the low-energy model incorporates the screen-ing effects from the high-energy bands, whereas the screenscreen-ing processes
within thet1ubands are excluded to avoid duplication because the latter
processes are taken into account when we solve the model. Such
par-tially screened Coulomb parameters are calculated (26) with the
Fig. 4. Double occupancy, size of spin, weights of intramolecular configurations, spectral functions at 40 K, and schematic pictures of repre-sentative intramolecular configurations. (A) Volume dependence of the double-occupancy D =〈ni↑ni↓〉 (red), the interorbital interspin correlation 〈ni↑nj↓〉 (green), and the size S of the spin per molecule (blue). (B) Spectral functions of several fcc A3C60systems at 40 K. For comparison, we show the DFT density
of states for fcc K3C60(VC603−= 722 Å
3) as the shaded area. (C) Weights of several onsite configurations appearing in the quantum Monte Carlo simulations.
(210) [(111)] generically denotes the configurations of {n1,n2,n3} = {2,1,0}, {0,2,1}, {1,0,2}, {2,0,1}, {1,2,0}, {0,1,2} [{n1,n2,n3} = {1,1,1}], with nibeing the
occu-pation of orbital i. N≠ 3 with N = n1+ n2+ n3denotes the configurations away from half filling. (D) Illustrative pictures for the (111) and (210)
config-urations. The up and down arrows indicate the up- and down-spin electrons, respectively.
on May 24, 2017
http://advances.sciencemag.org/
cRPA (31). Similarly, we calculate renormalized electron-phonon
coupling gijnðk;qÞ and phonon frequency wqnby applying the recently
developed cDFPT (24).
In the partition function for the lattice Hamiltonian (Eq.1) written
in the coherent state path integral formalism, we can integrate out the phonon degrees of freedom. This results in an electronic model with
the additional electron-electron interaction (Uph, U′ph, andJph)
mediated by phonons on top of the cRPA Coulomb interaction. The
onsite phonon-mediated interaction Vij;i′j′ (withUph =Vii,ii,U′ph=
Vii,jj,Jph=Vij,ij=Vij,ji) is given, on the Matsubara axis, by (24): Vij;i′j′ðiWnÞ ¼ −
∑
qng∼ijðq; nÞ 2wqnW2 nþ w2qn
g∼ i′j′ðq; nÞ;
whereWn= 2npT is the bosonic Matsubara frequency andg∼ijðq; nÞ ¼ 1
Nk
∑
kg nijðk; qÞ with the number Nkofk-points. Here, the sum over the phonon branches runs from 1 to 189. In practice, we omit the lowest 9 branches [n = 1 to 9, which correspond to the acoustic modes, the librations, and the alkali-ion vibrations at the octahedral sites (20)]. This is justified because the coupling between these modes and thet1uelectrons is tiny (2).
We solve the derived lattice Hamiltonian by means of the E-DMFT
(22), which maps the Hamiltonian (Eq. 1) onto a three-orbital
single-impurity model embedded in noninteracting bath subject to self-consistent conditions. In the mapping, the E-DMFT incorporates the dynamical screening through the off-site interactions into the
on-site interactions (UVandU′V) in a self-consistent way. To solve the
impurity model, we use the continuous-time quantum Monte Carlo
method based on the strong coupling expansion (32). Further detail
can be found in Sections C and D in the Supplementary Materials.
The frequency dependence ofUVandU′Vin Fig. 3 is calculated with
the Padé analytic continuation. We perform the analytic continuation
ontow + ih with h = 0.01 eV from the data along the Matsubara axis at
40 K for Cs3C60with VC3
60 ¼ 762 Å
3. The spectral functions in Fig. 4B
are calculated with the maximum entropy method.
SUPPLEMENTARY MATERIALS
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/ content/full/1/7/e1500568/DC1
Text (Sections A to F)
Fig. S1. Frequency dependence of partially screened Coulomb interactions for fcc Cs3C60with
VC3 60 = 762Å
3.
Fig. S2. Frequency dependence of the superconducting gap function at 10 K. Table S1. Summary of input parameters for the E-DMFT calculations. Table S2. Stability of superconducting (SC) solution at 10 K. References (33–49)
REFERENCES AND NOTES
1. A. F. Hebard, M. J. Rosseinsky, R. C. Haddon, D. W. Murphy, S. H. Glarum, T. T. M. Palstra, A. P. Ramirez, A. R. Kortan, Superconductivity at 18 K in potassium-doped C60. Nature
350, 600–601 (1991).
2. O. Gunnarsson, Alkali-Doped Fullerides: Narrow-Band Solids with Unusual Properties (World Scientific Publishing Co. Pte. Ltd., Singapore, 2004).
3. A. Y. Ganin, Y. Takabayashi, Y. Z. Khimyak, S. Margadonna, A. Tamai, M. J. Rosseinsky, K. Prassides, Bulk superconductivity at 38 K in a molecular system. Nat. Mater. 7, 367–371 (2008). 4. Y. Takabayashi, A. Y. Ganin, P. Jeglič, D. Arčon, T. Takano, Y. Iwasa, Y. Ohishi, M. Takata,
N. Takeshita, K. Prassides, M. J. Rosseinsky, The disorder-free non-BCS superconductor Cs3C60
emerges from an antiferromagnetic insulator parent state. Science 323, 1585–1590 (2009).
5. A. Y. Ganin, Y. Takabayashi, P. Jeglič, D. Arčon, A. Potočnik, P. J. Baker, Y. Ohishi, M. T. McDonald, M. D. Tzirakis, A. McLennan, G. R. Darling, M. Takata, M. J. Rosseinsky, K. Prassides, Polymorphism control of superconductivity and magnetism in Cs3C60close to the Mott transition. Nature 466,
221–225 (2010).
6. Y. Ihara, H. Alloul, P. Wzietek, D. Pontiroli, M. Mazzani, M. Riccò, NMR study of the Mott transitions to superconductivity in the two Cs3C60phases. Phys. Rev. Lett. 104, 256402
(2010).
7. Y. Ihara, H. Alloul, P. Wzietek, D. Pontiroli, M. Mazzani, M. Riccò, Spin dynamics at the Mott transition and in the metallic state of the Cs3C60superconducting phases. Europhys. Lett.
94, 37007 (2011).
8. P. Wzietek, T. Mito, H. Alloul, D. Pontiroli, M. Aramini, M. Riccò, NMR study of the super-conducting gap variation near the Mott transition in Cs3C60. Phys. Rev. Lett. 112, 066401
(2014).
9. R. H. Zadik, Y. Takabayashi, G. Klupp, R. H. Colman, A. Y. Ganin, A. Potočnik, P. Jeglič, D. Arčon, P. Matus, K. Kamarás, Y. Kasahara, Y. Iwasa, A. N. Fitch, Y. Ohishi, G. Garbarino, K. Kato, M. J. Rosseinsky, K. Prassides, Optimized unconventional superconductivity in a molecular Jahn-Teller metal. Sci. Adv. 1, e1500059 (2015).
10. G. Klupp, P. Matus, K. Kamarás, A. Y. Ganin, A. McLennan, M. J. Rosseinsky, Y. Takabayashi, M. T. McDonald, K. Prassides, Dynamic Jahn-Teller effect in the parent insulating state of the molecular superconductor Cs3C60. Nat. Commun. 3, 912 (2012).
11. C. M. Varma, J. Zaanen, K. Raghavachari, Superconductivity in the fullerenes. Science 254, 989–992 (1991).
12. M. Schluter, M. Lannoo, M. Needels, G. A. Baraff, D. Tománek, Electron-phonon coupling and superconductivity in alkali-intercalated C60solid. Phys. Rev. Lett. 68, 526–529 (1992).
13. I. I. Mazin II, O. V. Dolgov, A. Golubov, S. V. Shulga, Strong-coupling effects in alkali-metal-doped C60. Phys. Rev. B Condens. Matter 47, 538–541 (1993).
14. F. C. Zhang, M. Ogata, T. M. Rice, Attractive interaction and superconductivity for K3C60.
Phys. Rev. Lett. 67, 3452–3455 (1991).
15. S. Chakravarty, M. P. Gelfand, S. Kivelson, Electronic correlation effects and super-conductivity in doped fullerenes. Science 254, 970–974 (1991).
16. S. Suzuki, S. Okada, K. Nakano, Theoretical study on the superconductivity induced by the dynamic Jahn-Teller effect in alkali-metal-doped C60. J. Phys. Soc. Jpn. 69, 2615–2622
(2000).
17. M. Capone, M. Fabrizio, C. Castellani, E. Tosatti, Strongly correlated superconductivity. Science 296, 2364–2366 (2002).
18. M. Capone, M. Fabrizio, C. Castellani, E. Tosatti, Colloquium: Modeling the unconventional superconducting properties of expanded A3C60fullerides. Rev. Mod. Phys. 81, 943–958
(2009).
19. J. E. Han, O. Gunnarsson, V. H. Crespi, Strong superconductivity with local Jahn-Teller phonons in C60solids. Phys. Rev. Lett. 90, 167006 (2003).
20. R. Akashi, R. Arita, Nonempirical study of superconductivity in alkali-doped fullerides based on density functional theory for superconductors. Phys. Rev. B 88, 054510 (2013). 21. J. L. Janssen, M. Côté, S. G. Louie, M. L. Cohen, Electron-phonon coupling in C60using
hybrid functionals. Phys. Rev. B Condens. Matter 81, 073106 (2010).
22. G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, C. A. Marianetti, Electronic structure calculations with dynamical mean-field theory. Rev. Mod. Phys. 78, 865–951 (2006).
23. N. Marzari, D. Vanderbilt, Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B Condens. Matter 56, 12847–12865 (1997).
24. Y. Nomura, K. Nakamura, R. Arita, Effect of electron-phonon interactions on orbital fluctuations in iron-based superconductors. Phys. Rev. Lett. 112, 027002 (2014).
25. K. Inaba, A. Koga, S.-i. Suga, N. Kawakami, Finite-temperature Mott transitions in the multi-orbital Hubbard model. Phys. Rev. B Condens. Matter 72, 085112 (2005).
26. Y. Nomura, K. Nakamura, R. Arita, Ab initio derivation of electronic low-energy models for C60and aromatic compounds. Phys. Rev. B Condens. Matter 85, 155452 (2012).
27. M. Capone, M. Fabrizio, E. Tosatti, Direct transition between a singlet Mott insulator and a superconductor. Phys. Rev. Lett. 86, 5361–5364 (2001).
28. M. Capone, M. Fabrizio, C. Castellani, E. Tosatti, Strongly correlated superconductivity and pseudogap phase near a multiband Mott insulator. Phys. Rev. Lett. 93, 047001 (2004). 29. H. Suhl, B. T. Matthias, L. R. Walker, Bardeen-Cooper-Schrieffer theory of superconductivity
in the case of overlapping bands. Phys. Rev. Lett. 3, 552–554 (1959).
30. J. Kondo, Superconductivity in transition metals. Prog. Theor. Phys. 29, 1–9 (1963). 31. F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Biermann, A. I. Lichtenstein,
Frequency-dependent local interactions and low-energy effective models from electronic structure calculations. Phys. Rev. B Condens. Matter 70, 195104 (2004).
32. P. Werner, A. Comanac, L. de’ Medici, M. Troyer, A. J. Millis, Continuous-time solver for quantum impurity models. Phys. Rev. Lett. 97, 076405 (2006).
33. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. D. Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov,
on May 24, 2017
http://advances.sciencemag.org/
P. Umari, R. M. Wentzcovitch, QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009). 34. J. P. Perdew, A. Zunger, Self-interaction correction to density-functional approximations
for many-electron systems. Phys. Rev. B 23, 5048–5079 (1981).
35. N. Troullier, J. L. Martins, Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B 43, 1993–2006 (1991).
36. L. Kleinman, D. M. Bylander, Efficacious form for model pseudopotentials. Phys. Rev. Lett. 48, 1425–1428 (1982).
37. S. G. Louie, S. Froyen, M. L. Cohen, Nonlinear ionic pseudopotentials in spin-density-functional calculations. Phys. Rev. B Condens. Matter 26, 1738–1742 (1982).
38. D. D. Koelling, B. N. Harmon, A technique for relativistic spin-polarised calculations. J. Phys. C Solid State Phys. 10, 3107–3114 (1977).
39. T. Fujiwara, S. Yamamoto, Y. Ishii, Generalization of the iterative perturbation theory and metal–insulator transition in multi-orbital Hubbard bands. J. Phys. Soc. Jpn. 72, 777–780 (2003). 40. Y. Nohara, S. Yamamoto, T. Fujiwara, Electronic structure of perovskite-type transition metal oxides LaMO3(M = Ti ~ Cu) by U + GW approximation. Phys. Rev. B Condens. Matter 79, 195110 (2009).
41. M. S. Golden, M. Knupfer, J. Fink, J. F. Armbruster, T. R. Cummins, H. A. Romberg, M. Roth, M. Sing, M. Schmidt, E. Sohmen, The electronic structure of fullerenes and fullerene compounds from high-energy spectroscopy. J. Phys. Condens. Matter 7, 8219–8247 (1995). 42. A. M. Sengupta, A. Georges, Non-Fermi-liquid behavior near a T=0 spin-glass transition.
Phys. Rev. B Condens. Matter 52, 10295–10302 (1995).
43. Q. Si, J. L. Smith, Kosterlitz-Thouless transition and short range spatial correlations in an extended Hubbard model. Phys. Rev. Lett. 77, 3391–3394 (1996).
44. P. Sun, G. Kotliar, Extended dynamical mean-field theory and GW method. Phys. Rev. B Condens. Matter 66, 085120 (2002).
45. T. Ayral, S. Biermann, P. Werner, Screening and nonlocal correlations in the extended Hubbard model from self-consistent combined GW and dynamical mean field theory. Phys. Rev. B Condens. Matter 87, 125149 (2013).
46. I. G. Lang, Yu. A. Firsov, Kinetic theory of semiconductors with low mobility. Sov. J. Exp. Theor. Phys. 16, 1301 (1963).
47. P. Werner, A. J. Millis, Efficient dynamical mean field simulation of the Holstein-Hubbard model. Phys. Rev. Lett. 99, 146404 (2007).
48. K. Steiner. Y. Nomura, P. Werner, Double-expansion impurity solver for multiorbital models with dynamically screened U and J, arXiv:1506.01173.
49. A. Koga, P. Werner, Superconductivity in the two-band Hubbard model. Phys. Rev. B Condens. Matter 91, 085108 (2015).
Acknowledgments: We would like to thank K. Nakamura for valuable comments on the man-uscript, and Y. Iwasa and Y. Kasahara for fruitful discussions and for providing us with the experimental phase diagram. We acknowledge useful discussions with P. Werner, T. Ayral, Y. Murakami, H. Shinaoka, N. Parragh, G. Sangiovanni, M. Imada, A. Oshiyama, A. Fujimori, P. Wzietek, H. Alloul, M. Fabrizio, E. Tosatti, and G. Giovannetti. Some of the calculations were performed at the Super-computer Center, The Institute for Solid State Physics (ISSP), University of Tokyo. Funding: Y.N. is supported by Grant-in-Aid for JSPS Fellows (no. 12J08652) from Japan Society for the Promotion of Science (JSPS), Japan. S.S. is supported by Grant-in-Aid for Scientific Research (no. 26800179), from JSPS Japan. M.C. is supported by FP7/European Research Council (ERC) through the Starting Grant SUPERBAD (grant agreement no. 240524) and by the EU-Japan Project LEMSUPER (grant agreement no. 283214). Author contributions: Y.N. performed the calculations. All the authors discussed the calculated results and wrote the manuscript. M.C. and R.A. conceived the project. Competing interests: The authors declare that they have no competing interests.
Submitted 5 May 2015 Accepted 15 July 2015 Published 21 August 2015 10.1126/sciadv.1500568
Citation: Y. Nomura, S. Sakai, M. Capone, R. Arita, Unified understanding of superconductivity and Mott transition in alkali-doped fullerides from first principles. Sci. Adv. 1, e1500568 (2015).
on May 24, 2017
http://advances.sciencemag.org/
doi: 10.1126/sciadv.1500568 2015, 1:.
Sci Adv
(August 21, 2015)
Yusuke Nomura, Shiro Sakai, Massimo Capone and Ryotaro Arita
this article is published is noted on the first page.
This article is publisher under a Creative Commons license. The specific license under which
article, including for commercial purposes, provided you give proper attribution.
licenses, you may freely distribute, adapt, or reuse the
CC BY
For articles published under
.
here
Association for the Advancement of Science (AAAS). You may request permission by clicking for non-commerical purposes. Commercial use requires prior permission from the American
licenses, you may distribute, adapt, or reuse the article
CC BY-NC
For articles published under
http://advances.sciencemag.org. (This information is current as of May 24, 2017): The following resources related to this article are available online at
http://advances.sciencemag.org/content/1/7/e1500568.full
online version of this article at:
including high-resolution figures, can be found in the
Updated information and services,
http://advances.sciencemag.org/content/suppl/2015/08/20/1.7.e1500568.DC1
can be found at:
Supporting Online Material
http://advances.sciencemag.org/content/1/7/e1500568#BIBL
6 of which you can access for free at:
cites 47 articles,
This article
trademark of AAAS
otherwise. AAAS is the exclusive licensee. The title Science Advances is a registered York Avenue NW, Washington, DC 20005. Copyright is held by the Authors unless stated published by the American Association for the Advancement of Science (AAAS), 1200 New
(ISSN 2375-2548) publishes new articles weekly. The journal is
Science Advances
on May 24, 2017
http://advances.sciencemag.org/
